Computer Graphics - HDR & Tone Mapping - Hendrik Lensch Computer Graphics WS07/08 –Tone Mapping
Overview • Last time – Gamma Correction – Color spaces • Today – Terms and Definitions – Tone Mapping • Next lecture – Transformations Computer Graphics WS07/08 –Tone Mapping
Dynamic Range Dynamic 10 -6 10 -4 10 -2 10 0 10 2 10 4 10 6 10 8 Range Luminance [cd/m 2 ] 1:500 1:1500 1:30 Computer Graphics WS07/08 –Tone Mapping
Acquisition and Display of HDR • Luminance in real-world scenes -> HDR • Can be easily simulated • Acquisition with LDR cameras • Display on LDR monitors • HDR displays Computer Graphics WS07/08 –Tone Mapping
Exposure Bracketing – capture additional over and underexposed images Computer Graphics WS07/08 –Tone Mapping
Exposure Bracketing – capture additional over and underexposed images Computer Graphics WS07/08 –Tone Mapping
Exposure Bracketing – capture additional over and underexposed images – how much variation? – how to combine? Computer Graphics WS07/08 –Tone Mapping
Dynamic Range in Real World Images – natural scenes: 18 stops (2^18) – human: 17stops (after adaptation 30stops ~ 1:1,000,000,000) – camera: 10-16stops [Stumpfel et al. 00] Computer Graphics WS07/08 –Tone Mapping
Dynamic Range of Cameras example: photographic camera with standard CCD sensor • – dynamic range of sensor 1:1000 – exposure variation (handheld camera/non- static scene): 1/60 th s – 1/6000 th s exposure time 1:100 – varying aperture f/2.0 – f/22.0 ~1:100 – exposure bias/varying “sensitivity” 1:10 – total (sequential) 1:100,000,000 • simultaneous dynamic range still only 1:1000 • similar situation for analog cameras Computer Graphics WS07/08 –Tone Mapping
High Dynamic Range (HDR) Imaging basic idea of multi-exposure • techniques: – combine multiple images with different exposure settings – makes use of available sequential dynamic range other techniques available (e.g. • HDR video) Computer Graphics WS07/08 –Tone Mapping
OECF Test Chart • absolute calibration Computer Graphics WS07/08 –Tone Mapping
High Dynamic Range Imaging – limited dynamic range of cameras is a problem • shadows are underexposed • bright areas are overexposed • sampling density is not sufficient – some modern CMOS imagers have a higher and often sufficient dynamic range than most CCD imagers Computer Graphics WS07/08 –Tone Mapping
High Dynamic Range (HDR) Imaging – analog film with several emulsions of different sensitivity levels by Wyckoff in the 1960s • dynamic range of about 10 8 – commonly used method for digital photography by Debevec and Malik (1997) • selects a small number of pixels from the images • performs an optimization of the response curve with a smoothness constraint – newer method by Robertson et al. (1999) • optimization over all pixels in all images Computer Graphics WS07/08 –Tone Mapping
High Dynamic Range Imaging general idea of High Dynamic Range (HDR) imaging: – combine multiple images with different exposure times • pick for each pixel a well exposed image • response curve needs to be known • don’t change aperture due to different depth-of-field Computer Graphics WS07/08 –Tone Mapping
High Dynamic Range Imaging Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] Principle of this approach: Principle of this approach: • calculate a HDR image using the response curve calculate a HDR image using the response curve • • find a better response curve using the HDR image find a better response curve using the HDR image • (to be iterated until convergence) (to be iterated until convergence) Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] input: – series of i images with exposure times t i and pixel values y ij y = f t x ( ) ij i j task: – find irradiance (luminance) x j I y – recover response curve ( ) ij − = = f y t x I 1 ( ) ij i j y ij Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] input: – series of i images with exposure times t i and pixel values y ij – a weighting function w ij = w ij (y ij ) (bell shaped curve) – a camera response curve • initial assumption: linear response I y ⇒ calculate HDR values x j from images using ( ) ij ∑ w t I ij i y ij = x i ∑ j w t 2 ij i i Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] I ( m I y ) ( ) optimizing the response curve resp. : ij – minimization of objective function O = ∑ ij − O w I t x 2 ( ) ij y i j i j , using Gauss-Seidel relaxation yields 1 ∑ = I t x m i j E Card ( ) ∈ i j E m , m = = E i j y m {( , ) : } m ij – normalization of I so that I 128 =1.0 Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] both steps – calculation of a HDR image using I – optimization of I using the HDR image are now iterated until convergence • criterion: decrease of O below some threshold • usually about 5 iterations Computer Graphics WS07/08 –Tone Mapping
HDR Imaging [Robertson et al.99] I y log( ( )) ij Computer Graphics WS07/08 –Tone Mapping
Capturing Environment Maps 1/2000s 1/500s 1/125s 1/30s 1/8s 1/2000s 1/500s 1/125s 1/30s 1/8s series of input images series of input images Computer Graphics WS07/08 –Tone Mapping
Capturing Environment Maps series of input images series of input images Computer Graphics WS07/08 –Tone Mapping
Weighting Function • [Robertson et al.99] ⎛ ⎞ − y 2 ( 127 . 5 ) ⎜ ⎟ ij = − w exp 4 ⎜ ⎟ ij 2 127 . 5 ⎝ ⎠ choice of weighting function w(y ij ) for response • recovery – for 8 bit images – possible correction at both ends (over/underexposure) – motivated by general noise model Computer Graphics WS07/08 –Tone Mapping
Algorithm of Robertson et al. discussion • – method very easy – doesn’t make assumptions about response curve shape – converges fast – takes all available input data into account – can be extended to >8 bit color depth – 16bit should be followed by smoothing Computer Graphics WS07/08 –Tone Mapping
Input Images for Response Recovery my favorite: • – grey card, out of focus, smooth illumination gradient • advantages – uniform histogram of values – no color processing or sharpening interfering with the result Computer Graphics WS07/08 –Tone Mapping
Input Images for HDR Generation how many images are necessary to get good results? • – depends on scene dynamic range and on quality requirements – most often a difference of two stops (factor of 4) between exposures is sufficient – [Grossberg & Nayar 2003] Computer Graphics WS07/08 –Tone Mapping
HDR-Video – LDR [Bennett & McMillan 2005] – HDR image formats [OpenExr, HDR JPEG] – HDR MPEG Encoding [Mantiuk et al. 2004] – HDR + motion compensation [Kang et al. 2003] Computer Graphics WS07/08 –Tone Mapping
Tone-Mapping Computer Graphics WS07/08 –Tone Mapping
Terms and Definitions • Dynamic Range – Factor between the highest and the smallest representable value – Two strategies • Make white brighter • Make black darker • Contrast L C = max – Simple contrast S L Δ L min C = – Weber fraction (step fct.) W L | | min − L L max min C = – Michelson contrast (sinusoidal fct.) M L + L ⎛ ⎞ max min L ⎜ ⎟ max C = – Logarithmic ratio log ⎜ ⎟ L 10 L ⎝ ⎠ min ⎛ ⎞ L – Signal to noise ratio (SNR) ⎜ ⎟ ⋅ C = max 20 log ⎜ ⎟ SNR 10 L ⎝ ⎠ min – Best for HVS: C W and C L Computer Graphics WS07/08 –Tone Mapping
Contrast Discrimination • Experiments [Whittle 1986] – Including high contrast – Michelson does not work too well • Particularly for high contrast – Good fits for C W and C L – Simplified linear model for CL • Δ C L,simpl (C L ) = 0.038737*C L 0.537756 – [Mantiuk et al., 2006] C M C W C L Computer Graphics WS07/08 –Tone Mapping
Contrast Measurement • Contrast Detection Threshold – Smallest detectable contrast in a uniform field of view • Contrast Discrimination Threshold – Smallest visible difference between two similar signals – Works in the suprathreshold domain (signals above threshold) • Often sinusoidal or square wave pattern Computer Graphics WS07/08 –Tone Mapping
Why Tone-Mapping? • Mapping radiance to pixel values? – Luminance of typical desktop displays: • Up to a few 100 cd/m 2 – Luminance range for human visual perception • Min 10 -5 cd/m 2 Shadows under starlight • Max 10 5 cd/m 2 Snow in direct sun light • Goal – Compress the dynamic range of an input image – Reproduce human perception to closely match that of the real scene • Brightness and contrast • Adaptation of the eye to environment • Other issues (glare, color perception, resolution) Computer Graphics WS07/08 –Tone Mapping
Computer Graphics WS07/08 –Tone Mapping Example
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